Permutations an...

The area of the triangle formed by the straight line $$x+y=3$$ and the bisectors of the pair of straight lines $${ x }^{ 2 }-{ y }^{ 2 }+2y=1$$ is 

If the area of triangle formed by the points $$(2a, b) (a + b, 2b + a)$$ and $$(2b, 2a)$$ be $$\lambda$$, then the area of the triangle whose vertices are $$(a + b, a - b), (3b - a, b + 3a)$$ and $$(3a - b, 3b - a)$$ will be

If $$ (\sqrt{2x}+\sqrt{3y}^{2} -36(\sqrt{3x}-\sqrt{2y})^{2}=0$$ and $$\sqrt{2x}-\sqrt{3y}+4\sqrt{5}=0$$ represents an Issosceles traiangle with base angle $$tan^{-1}6$$ then its area is

If the area of triangle formed by the points (2a , b) (a + b , 2b + a) and (2b , 2a) be $$\lambda$$ , then the area of the triangle whose vertices are (a + b , a b) , (3b a , b + 3a) and (3a b , 3b a) will be

A triangle has two of its vertices at (0, 1) and (2, 2) in the cartesioan plane. Its third vertex lies on the x-axis. If the area of the triangle is 2 square units then the sum of the possible abscissae of the third vertex, is -

Let P and Q be points $$(4, 4)$$ and $$(9, 6)$$ of parabola $${y^2} = 4a\left( {x - b} \right)$$ If R be a point on the arc of the parabola between P and Q, such that the area of  $$\Delta PRQ$$ is largest, then R is

Area of the triangle formed by $${ (x }_{ 1 },{ y }_{ 1 })$$,$${ (x }_{ 2 },{ y }_{ 2 })$$,
$${ (3x }_{ 2 }-{ 2x }_{ 1 },{ 3y }_{ 2 }-{ 2y }_{ 1 })$$ is

The area of a triangle whose sides are $$ a , b $$ and $$ c $$ is

If $${ p }_{ 1 },{ p }_{ 2 },{ p }_{ 3 }$$ are the altitudes of a triangle from its vertices $$A,B,C$$ and $$\triangle $$, the area of the triangle $$ABC$$, then $$\frac { 1 }{ { p }_{ 1 } } +\frac { 1 }{ { p }_{ 2 } } +\frac { 1 }{ { p }_{ 3 } } $$ is equal to-

The arrangement of the areas of the triangles formed by the following points in ascending order is 
i) P(0,0), Q(4,0), R(0,3)
ii) P(0,0), Q(5,0), R(0,2)
iii) P(0,0), Q(0,5), R(6,0)
iv) p(3,0), Q(0,6), R(0,0)